test/yukicoder/362.test.cpp

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• Last update: 2024-10-11 11:57:14+09:00
• Problem: https://yukicoder.me/problems/no/362

Depends on

• オートマトン上のDP (src/Misc/Automaton.hpp)

Code

// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/362
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
#include <iostream>
#include <vector>
#include <array>
#include "src/Misc/Automaton.hpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 vector alp= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9};
 auto tr_le= [&](int64_t s, int c) { return (s - c + 10) / 10 - 1; };
 auto ac_le= [&](int64_t) { return true; };
 using state_t= array<int, 2>;
 auto tr_kado= [&](state_t s, int c) -> state_t {
  if (s[0] == -1) {
   if (s[1] == c) return {-2, -2};
   else return {s[1], c};
  }
  if (s[0] == c || s[1] == c) return {-2, -2};
  auto [mi, mx]= minmax({s[0], s[1], c});
  if (s[1] == mi || s[1] == mx) return {s[1], c};
  return {-2, -2};
 };
 auto ac_kado= [&](state_t s) { return true; };
 Automaton dfa_kado(alp, state_t{-1, -1}, tr_kado, ac_kado, state_t{-2, -2});
 auto tr_0= [&](bool, int c) -> bool { return c; };
 Automaton dfa_0(alp, false, tr_0, [](bool s) { return s; });
 auto dfa1= dfa_kado & dfa_0;
 int T;
 cin >> T;
 while (T--) {
  int64_t K;
  cin >> K;
  int64_t l= 101, h= 37294859064823;
  while (h - l > 1) {
   int64_t X= (h + l) / 2;
   int n= 0;
   for (auto m= X; m; m/= 10) ++n;
   Automaton dfa_le(alp, X, tr_le, ac_le, int64_t(-1));
   auto dfa= dfa1 & dfa_le;
   int64_t sum= dfa.num<int64_t>(n);
   for (int i= 3; i < n; ++i) sum+= dfa1.num<int64_t>(i);
   if (sum < K) l= X;
   else h= X;
  }
  cout << h << '\n';
 }
 return 0;
}

#line 1 "test/yukicoder/362.test.cpp"
// competitive-verifier: PROBLEM https://yukicoder.me/problems/no/362
// competitive-verifier: TLE 0.5
// competitive-verifier: MLE 64
#include <iostream>
#include <vector>
#include <array>
#line 2 "src/Misc/Automaton.hpp"
#include <type_traits>
#include <set>
#include <map>
#include <unordered_map>
#line 7 "src/Misc/Automaton.hpp"
#include <algorithm>
#include <queue>
#include <cstdlib>
#include <cassert>
template <class symbol_t> class Automaton {
 std::vector<int> table;
 std::vector<int8_t> info;
 std::vector<symbol_t> alph;
 const int m;
 template <class Map, class state_t, class F, class G, class H> void build(const state_t &initial_state, const F &transition, const G &is_accept, const H &abs_reject) {
  static_assert(std::is_same_v<bool, std::invoke_result_t<G, state_t>>);
  static_assert(std::is_same_v<bool, std::invoke_result_t<H, state_t>>);
  Map encode;
  std::vector<state_t> decode;
  int ts= 0;
  decode.push_back(initial_state), encode.emplace(initial_state, ts++);
  for (int i= 0, k= 0; i < ts; ++i) {
   auto s= decode[i];
   table.resize(table.size() + m);
   for (int j= 0; j < m; ++j) {
    if (auto t= transition(s, j); abs_reject(t)) table[k++]= -1;
    else if (auto it= encode.find(t); it != encode.end()) table[k++]= it->second;
    else table[k++]= ts, decode.push_back(t), encode.emplace(t, ts++);
   }
  }
  info.resize(ts);
  for (int i= ts; i--;) info[i]= is_accept(decode[i]);
 }
 Automaton(const std::vector<symbol_t> &alphabet): alph(alphabet), m(alph.size()) {}
public:
 template <class state_t, class F, class G, std::enable_if_t<std::is_invocable_r_v<state_t, F, state_t, symbol_t>, std::nullptr_t> = nullptr> Automaton(const std::vector<symbol_t> &alphabet, const state_t &initial_state, const F &transition, const G &is_accept): alph(alphabet), m(alph.size()) {
  std::sort(alph.begin(), alph.end());
  auto tr= [&](const state_t &s, int i) { return transition(s, alph[i]); };
  auto rej= [](const state_t &) { return false; };
  if constexpr (std::is_integral_v<state_t>) build<std::unordered_map<state_t, int>, state_t>(initial_state, tr, is_accept, rej);
  else build<std::map<state_t, int>, state_t>(initial_state, tr, is_accept, rej);
 }
 template <class state_t, class F, class G, std::enable_if_t<std::is_invocable_r_v<state_t, F, state_t, symbol_t>, std::nullptr_t> = nullptr> Automaton(const std::vector<symbol_t> &alphabet, const state_t &initial_state, const F &transition, const G &is_accept, const state_t &abs_rej_state): alph(alphabet), m(alph.size()) {
  std::sort(alph.begin(), alph.end());
  auto tr= [&](const state_t &s, int i) { return transition(s, alph[i]); };
  auto rej= [abs_rej_state](const state_t &s) { return s == abs_rej_state; };
  if constexpr (std::is_integral_v<state_t>) build<std::unordered_map<state_t, int>, state_t>(initial_state, tr, is_accept, rej);
  else build<std::map<state_t, int>, state_t>(initial_state, tr, is_accept, rej);
 }
 template <class state_t, class F, class G, std::enable_if_t<std::is_invocable_r_v<std::set<state_t>, F, state_t, symbol_t>, std::nullptr_t> = nullptr> Automaton(const std::vector<symbol_t> &alphabet, const state_t &initial_state, const F &transition, const G &is_accept): alph(alphabet), m(alph.size()) {
  static_assert(std::is_same_v<bool, std::invoke_result_t<G, state_t>>);
  std::sort(alph.begin(), alph.end());
  auto tr= [&](const std::set<state_t> &s, int i) {
   std::set<state_t> ret;
   for (const auto &x: s) {
    auto ys= transition(x, alph[i]);
    ret.insert(ys.begin(), ys.end());
   }
   return ret;
  };
  auto ac= [&](const std::set<state_t> &s) { return std::any_of(s.begin(), s.end(), is_accept); };
  auto rej= [](const std::set<state_t> &s) { return s == std::set<state_t>(); };
  build<std::map<std::set<state_t>, int>, std::set<state_t>>(std::set<state_t>({initial_state}), tr, ac, rej);
 }
 template <class state_t, class F, class G, class H, std::enable_if_t<std::is_invocable_r_v<std::set<state_t>, F, state_t, symbol_t>, std::nullptr_t> = nullptr> Automaton(const std::vector<symbol_t> &alphabet, const state_t &initial_state, const F &transition, const G &is_accept, const H &eps_trans): alph(alphabet), m(alph.size()) {
  static_assert(std::is_same_v<bool, std::invoke_result_t<G, state_t>>);
  static_assert(std::is_same_v<std::set<state_t>, std::invoke_result_t<H, state_t>>);
  std::sort(alph.begin(), alph.end());
  auto eps_closure= [&](std::set<state_t> s) {
   for (std::set<state_t> t; s != t;) {
    t= s;
    for (const auto &x: t) {
     auto ys= eps_trans(x);
     s.insert(ys.begin(), ys.end());
    }
   }
   return s;
  };
  auto tr= [&](const std::set<state_t> &s, int i) {
   std::set<state_t> ret;
   for (const auto &x: s) {
    auto ys= transition(x, alph[i]);
    ret.insert(ys.begin(), ys.end());
   }
   return eps_closure(ret);
  };
  auto ac= [&](const std::set<state_t> &s) { return std::any_of(s.begin(), s.end(), is_accept); };
  auto rej= [](const std::set<state_t> &s) { return s == std::set<state_t>(); };
  build<std::map<std::set<state_t>, int>, std::set<state_t>>(eps_closure({initial_state}), tr, ac, rej);
 }
 Automaton operator&(const Automaton &r) const {
  assert(alph == r.alph);
  const int S= info.size();
  auto tr= [&](int s, int q) {
   auto [s1, s0]= std::div(s, S);
   int t1= r.table[s1 * m + q], t0= table[s0 * m + q];
   return t0 == -1 || t1 == -1 ? -1 : t1 * S + t0;
  };
  auto ac= [&](int s) {
   auto [s1, s0]= std::div(s, S);
   return info[s0] == 1 && r.info[s1] == 1;
  };
  auto rej= [](int s) { return s == -1; };
  Automaton ret(alph);
  return ret.build<std::unordered_map<int, int>, int>(0, tr, ac, rej), ret;
 }
 template <class T, class A, class F> T dp_run(int n, const A &op, const T &ti, const F &f, const T &init) const {
  static_assert(std::is_same_v<T, std::invoke_result_t<A, T, T>>);
  static_assert(std::is_same_v<T, std::invoke_result_t<F, T, symbol_t, int>>);
  const size_t S= info.size();
  std::queue<std::pair<int, int>> que;
  T dp[2][S], ret= ti;
  bool in[2][S];
  for (std::fill_n(dp[0], S, ti), std::fill_n(dp[1], S, ti), std::fill_n(in[0], S, 0), std::fill_n(in[1], S, 0), dp[0][0]= init, que.emplace(0, 0), in[0][0]= 1; que.size();) {
   auto [s, i]= que.front();
   bool b= i & 1;
   T tmp= dp[b][s];
   if (que.pop(), in[b][s]= 0, dp[b][s]= ti; i == n) {
    if (info[s] == 1) ret= op(ret, tmp);
    continue;
   }
   auto l= table.cbegin() + s * m;
   for (int j= m; j--;)
    if (int t= l[j]; t != -1)
     if (dp[!b][t]= op(dp[!b][t], f(tmp, alph[j], i)); !in[!b][t]) que.emplace(t, i + 1), in[!b][t]= 1;
  }
  return ret;
 }
 template <class T> T num(int n) const {
  return dp_run(n, [](const T &l, const T &r) { return l + r; }, T(), [](const T &x, const auto &, auto) { return x; }, T(1));
 }
};
#line 8 "test/yukicoder/362.test.cpp"
using namespace std;
signed main() {
 cin.tie(0);
 ios::sync_with_stdio(0);
 vector alp= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9};
 auto tr_le= [&](int64_t s, int c) { return (s - c + 10) / 10 - 1; };
 auto ac_le= [&](int64_t) { return true; };
 using state_t= array<int, 2>;
 auto tr_kado= [&](state_t s, int c) -> state_t {
  if (s[0] == -1) {
   if (s[1] == c) return {-2, -2};
   else return {s[1], c};
  }
  if (s[0] == c || s[1] == c) return {-2, -2};
  auto [mi, mx]= minmax({s[0], s[1], c});
  if (s[1] == mi || s[1] == mx) return {s[1], c};
  return {-2, -2};
 };
 auto ac_kado= [&](state_t s) { return true; };
 Automaton dfa_kado(alp, state_t{-1, -1}, tr_kado, ac_kado, state_t{-2, -2});
 auto tr_0= [&](bool, int c) -> bool { return c; };
 Automaton dfa_0(alp, false, tr_0, [](bool s) { return s; });
 auto dfa1= dfa_kado & dfa_0;
 int T;
 cin >> T;
 while (T--) {
  int64_t K;
  cin >> K;
  int64_t l= 101, h= 37294859064823;
  while (h - l > 1) {
   int64_t X= (h + l) / 2;
   int n= 0;
   for (auto m= X; m; m/= 10) ++n;
   Automaton dfa_le(alp, X, tr_le, ac_le, int64_t(-1));
   auto dfa= dfa1 & dfa_le;
   int64_t sum= dfa.num<int64_t>(n);
   for (int i= 3; i < n; ++i) sum+= dfa1.num<int64_t>(i);
   if (sum < K) l= X;
   else h= X;
  }
  cout << h << '\n';
 }
 return 0;
}

Test cases

Env	Name	Status	Elapsed	Memory
g++-13	0_1_sample.txt	AC	34 ms	4 MB
g++-13	0_2_sample.txt	AC	28 ms	4 MB
g++-13	1_1.txt	AC	28 ms	4 MB
g++-13	1_2.txt	AC	17 ms	4 MB
g++-13	1_3.txt	AC	11 ms	4 MB
g++-13	1_4.txt	AC	43 ms	4 MB
g++-13	1_5.txt	AC	77 ms	4 MB
g++-13	1_6.txt	AC	46 ms	4 MB
g++-13	1_7.txt	AC	65 ms	4 MB
g++-13	1_8.txt	AC	106 ms	4 MB
g++-13	1_9.txt	AC	146 ms	4 MB
g++-13	2_1.txt	AC	138 ms	4 MB
g++-13	2_2.txt	AC	140 ms	4 MB
g++-13	2_3.txt	AC	144 ms	4 MB
g++-13	2_4.txt	AC	138 ms	4 MB
g++-13	2_5.txt	AC	142 ms	4 MB
g++-13	3_1.txt	AC	135 ms	4 MB
g++-13	3_2.txt	AC	117 ms	4 MB
g++-13	3_3.txt	AC	147 ms	4 MB
g++-13	3_4.txt	AC	63 ms	4 MB
g++-13	3_5.txt	AC	150 ms	4 MB
g++-13	4_1_sample.txt	AC	20 ms	4 MB
clang++-18	0_1_sample.txt	AC	32 ms	4 MB
clang++-18	0_2_sample.txt	AC	26 ms	4 MB
clang++-18	1_1.txt	AC	26 ms	4 MB
clang++-18	1_2.txt	AC	16 ms	4 MB
clang++-18	1_3.txt	AC	10 ms	4 MB
clang++-18	1_4.txt	AC	40 ms	4 MB
clang++-18	1_5.txt	AC	72 ms	4 MB
clang++-18	1_6.txt	AC	44 ms	4 MB
clang++-18	1_7.txt	AC	60 ms	4 MB
clang++-18	1_8.txt	AC	97 ms	4 MB
clang++-18	1_9.txt	AC	135 ms	4 MB
clang++-18	2_1.txt	AC	127 ms	4 MB
clang++-18	2_2.txt	AC	127 ms	4 MB
clang++-18	2_3.txt	AC	131 ms	4 MB
clang++-18	2_4.txt	AC	126 ms	4 MB
clang++-18	2_5.txt	AC	133 ms	4 MB
clang++-18	3_1.txt	AC	126 ms	4 MB
clang++-18	3_2.txt	AC	108 ms	4 MB
clang++-18	3_3.txt	AC	135 ms	4 MB
clang++-18	3_4.txt	AC	58 ms	4 MB
clang++-18	3_5.txt	AC	138 ms	4 MB
clang++-18	4_1_sample.txt	AC	20 ms	4 MB

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